Surface Reconstruction Using Alpha Shapes

Abstract

We describe a method for reconstructing an unknown surface from a set of data points. The basic approach is to extract the surface as a polygon mesh from an ?-shape. Even though alpha shapes are generalized polytopes having complicated internal structures, we show that manifold surfaces, with or without boundaries, can be efficiently generated, and these surfaces completely describe the ?-shapes to the extent that they are visible from outside. Unlike the original ?-shapes, the polygonal surfaces can be easily simplified to yield compact models suitable for a variety of geometric modeling applications such as surface fitting.